In-medium Corrections Research Articles

Freezing-in a hot bath: resonances, medium effects and phase transitions

Relic density calculations of dark matter freezing out from the primordial plasma have reached a high level of sophistication, with several numerical tools readily available that match the observationally required accuracy. Dark matter production via the freeze-in mechanism, on the other hand, is sensitive to much higher temperatures than in the freeze-out case, implying both technical and computational difficulties when aiming for the same level of precision. We revisit the formulation of freeze-in production in a way that facilitates the inclusion of in-medium corrections like plasma effects and the spin statistics of relativistic quantum gases, as well as the temperature dependence of dark matter production rates induced by the electroweak and strong phase transitions, and we discuss in detail the additional complications arising in the presence of s-channel resonances. We illustrate our approach in the context of Higgs portal models, and provide the most accurate calculation to date of the freeze-in abundance of Scalar Singlet dark matter. We explore in particular the case of small reheating temperatures, for which the couplings implied by the freeze-in mechanism may be testable at the LHC. Together with this article we present a major update 6.3 of DarkSUSY with the added capability of performing general freeze-in calculations, including all complications mentioned above.

Light element (Z=1,2) production from spontaneous ternary fission of ^{252}Cf

The yields of light elements (Z=1,2) obtained from spontaneous ternary fission of ^{252}Cf are treated within a nonequilibrium approach, and the contribution of unstable nuclei and excited bound states is taken into account. These light cluster yields may be used to probe dense matter, and to infer in-medium corrections such as Pauli blocking which is determined by the nucleon density. Continuum correlations are calculated from scattering phase shifts using the Beth-Uhlenbeck formula, and the effect of medium modification is estimated. The relevant distribution is reconstructed from the measured yields of isotopes. This describes the state of the nucleon system at scission and cluster formation, using only three Lagrange parameters which are the nonequilibrium counterparts of the temperature and chemical potentials, as defined in thermodynamic equilibrium. We concluded that a simple nuclear statistical equilibrium model neglecting continuum correlations and medium effects is not able to describe the measured distribution of H and He isotopes. Moreover, the freeze-out concept may serve as an important ingredient to the nonequilibrium approach using the relevant statistical operator concept.

In-medium and isospin effects on eta production in heavy-ion collisions near threshold energies

The dynamics of $ \eta$ meson produced in heavy-ion collisions has been investigated within the Lanzhou quantum molecular dynamics model (LQMD). The in-medium corrections have been considered in the model, in which an attractive $ \eta$ -nucleon potential is implemented. The impacts of the $ \eta$ optical potential and the nuclear symmetry energy on the $ \eta$ dynamics are investigated. It is found that the total yields are slightly influenced by the potential and weakly depend on the symmetry energy. However, the structure of the kinetic spectra is related to the optical potential and the stiffness of symmetry energy. The attractive potential leads to the reduction of high-momentum (kinetic energy) $ \eta$ production, i.e., the spectra of momentum and transverse mass distributions, increasing the reabsorption process by surrounding nucleons, and favoring the in-plane eta emissions. The reabsorption process in $ \eta$ -nucleon collisions plays a significant role on the $ \eta$ dynamics.

Effects of in-medium nucleon-nucleon cross sections on stopping observable and ratio of free protons in heavy-ion collisions at 400 MeV/nucleon

The effects of in-medium nucleon-nucleon cross sections on the stopping observable and ratio of free protons in heavy-ion collisions at 400MeV/nucleon have been investigated within the framework of the IQMD+GEMINI model. Five kinds of in-medium corrections of nucleon-nucleon cross sections, which are considerably different in the referred energy and density, have been used in the model. It has been found that calculations of the stopping decrease when the in-medium cross sections decrease. Moreover, the ratio of free protons Rp depends not only on the value of the in-medium factors but also on its isospin dependence. In order to investigate the isospin effect of in-medium factors on the ratio of free protons Rp, the isospin dependence of in-medium factors has been adjusted and used in the model. The calculations have shown that the isospin dependence of in-medium factors does not impact the stopping, but impacts the ratio of free protons Rp. When the in-medium factors relation f nn med > f pp med is used in the model, the calculated values of Rp are larger than those in the f nn med < f pp med case.

In-medium and isospin effects on particle production near threshold energies in heavy-ion collisions

Dynamics of pseudoscalar mesons ($\pi$, $\eta$, $K$ and $\overline{K}$ ) and hyperons ($\Lambda$ and $\Sigma$) produced in heavy-ion collisions near threshold energies has been investigated within the Lanzhou quantum molecular dynamics (LQMD) transport model. The in-medium modifications on particle production in dense nuclear matter are implemented in the model through corrections on the elementary cross sections and by inclusion of the meson (hyperon)-nucleon potentials, in which the isospin effects are considered. It is found that the transportation of particles are influenced with the in-medium corrections. The total number of pions is reduced with an isospin, density and momentum dependent pion-nucleon potential. However, the ratios of charged pions is enhanced with inclusion of the potential. The production of eta in the domain of mid-rapidities and high momenta is sensitive to the $\eta$-nucleon potential, but weakly depends on symmetry energy. The attractive antikaon-nucleon potential enhances the subthreshold $\overline{K}$ production and also influences the structure of phase-space distributions. Dynamics of etas, kaons, antikaons and hyperons is also influenced by the pion potential because of collisions between pions and nucleons (resonances). The impacts of mean-field potentials on particle dynamics are investigated, such as the phase-space distributions from rapidity and transverse momentum spectra, inclusive invariant spectra, collective flows etc.

In-medium nuclear cluster energies within the extended Thomas-Fermi approach

A recently introduced analytical model for the nuclear density profile[1] is implemented in the Extended Thomas-Fermi (ETF) energy density functional. This allows to (i) shed a new light on the issue of the sign of surface symmetry energy in nuclear mass formulas, which is strongly related to the non-uniformity of the isospin asymmetry in finite nuclei, as well as to (ii) evaluate the in-medium corrections to the nuclear cluster energies in thermodynamic conditions relevant for the description of the (proto)-neutron star crust. The ground state configurations of the model are compared to Hartree-Fock calculations in spherical symmetry for some selected isotopic chains, and systematic errors are quantified. The in-medium modification of the nuclear mass due to the presence of a gas component is shown to strongly depend both on the density and the asymmetry of the nucleon gas. This shows the importance of accounting for such effects in the realistic modelizations of the equation of state for core-collapse supernovae and proto-neutron stars.

Quantum statistical calculation of cluster abundances in hot dense matter

The cluster abundances are calculated from a quantum statistical approach taking into account in-medium corrections. For arbitrary cluster size the self-energy and Pauli blocking shifts are considered. Exploratory calculations are performed for symmetric matter at temperature T = 5 MeV and baryon density ϱ = 0.0156 fm−3 to be compared with the solar element distribution. It is shown that the abundances of weakly bound nuclei with mass number 4 < A < 12 are strongly suppressed due to Pauli blocking effects.

The chiral quark condensate and pion decay constant in nuclear matter at next-to-leading order

Making use of the recently developed chiral power counting for the physics of nuclear matter (Oller et al 2010 J. Phys. G: Nucl. Part. Phys. 37 015106, Lacour et al Ann. Phys. at press), we evaluate the in-medium chiral quark condensate up to next-to-leading order for both symmetric nuclear matter and neutron matter. Our calculation includes the full in-medium iteration of the leading order local and one-pion exchange nucleon–nucleon interactions. Interestingly, we find a cancellation between the contributions stemming from the quark mass dependence of the nucleon mass appearing in the in-medium nucleon–nucleon interactions. Only the contributions originating from the explicit quark mass dependence of the pion mass survive. This cancellation is the reason of previous observations concerning the dominant role of the long-range pion contributions and the suppression of short-range nucleon–nucleon interactions. We find that the linear density contribution to the in-medium chiral quark condensate is only slightly modified for pure neutron matter by the nucleon–nucleon interactions. For symmetric nuclear matter, the in-medium corrections are larger, although smaller compared to other approaches due to the full iteration of the lowest order nucleon–nucleon tree-level amplitudes. Our calculation satisfies the Hellmann–Feynman theorem to the order worked out. Also we address the problem of calculating the leading in-medium corrections to the pion decay constant. We find that there are no extra in-medium corrections that violate the Gell-Mann–Oakes–Renner relation up to next-to-leading order.

The In-Medium \barK NInteraction within a Chiral Unitary Approach

The s- and p-wave contributions to the \barK N interaction in dense nuclear matter are obtained using a chiral unitary approach. We perform a self-consistent calculation of the \barK self-energy including Pauli blocking effects, meson self-energies modified by short-range correlations and baryon binding potentials. We find that the on-shell factorization cannot be applied to evaluate the in-medium corrections to p-wave amplitudes. Furthermore, the Λ and Σ develop a mass shift of -30 MeV at saturation density while the Σ* width increases to 80 MeV. We conclude that no deep and narrow \barK bound states could be observed.

Chiral approach to antikaons- andp-wave interactions in dense nuclear matter

The properties of the antikaons in nuclear matter are investigated from a chiral unitary approach which incorporates the $s$- and $p$-waves of the $\overline{K}N$ interaction. To obtain the in-medium meson-baryon amplitudes we include, in a self-consistent way, Pauli blocking effects, meson self-energies corrected by nuclear short-range correlations and baryon binding potentials. We pay special attention to investigating the validity of the on-shell factorization, showing that it cannot be applied in the evaluation of the in-medium corrections to the $p$-wave amplitudes. In nuclear matter at saturation energy, the \ensuremath{\Lambda} and \ensuremath{\Sigma} develop an attractive potential of about \ensuremath{-}30 MeV, while the ${\ensuremath{\Sigma}}^{*}$ pole remains at the free space value although its width gets sensibly increased to about 80 MeV. The antikaon also develops a moderate attraction that does not support the existence of very deep and narrow bound states, confirming the findings of previous self-consistent calculations.

Branching ratio change inK−absorption at rest and the nature of the Λ(1405)

We investigate in-medium corrections to the branching ratio in ${K}^{\ensuremath{-}}$ absorption at rest and their effect on the charged pion ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ spectrum. The in-medium corrections are due to Pauli blocking, which arises if the \ensuremath{\Lambda}(1405) is assumed to be a $\overline{K}$-nucleon bound state and leads to a density- and momentum-dependent mass shift of the \ensuremath{\Lambda}(1405). Requiring that the optical potential and the branching ratio are derived from the same elementary $T$ matrix, we find that the in-medium--corrected, density-dependent $T$ matrix gives a better description of the ${K}^{\ensuremath{-}}$ absorption reaction than the free, density-independent one. This result suggests that the dominant component of the \ensuremath{\Lambda}(1405) wave function is the $\overline{K}N$ bound state.

In-medium kaon production at the mean-field level

The in-medium mass and energy of kaons and antikaons are studied within the relativistic mean-field approach compatible with kaon-nucleon scattering data and are compared with predictions from chiral models. Implications for the subthreshold production of kaons and antikaons in heavy-ion collisions are discussed. On the mean-field level we find only small in-medium corrections for the relevant kaon production processes. The production of kaons is even less favourable at high density due to repulsive vector interactions. We conclude that one has to go beyond the mean-field level and take fluctuations and secondary production processes via resonances into account to explain the recently observed enhancement of kaon production at subthreshold energies. The situation is different for antikaons where in-medium effects strongly enhance their production rates. We also see strong in-medium modifications of the absorption processes for antikaons and Λ's which might be visible in flow measurements. We predict that at high density the threshold energy for antikaon and Λ production as well as for the annihilation become equal leading to similar numbers of antikaons and Λ's in the dense zone of a relativistic heavy-ion collision.

Comment on “Influence of the in-medium pion dispersion relation in heavy ion collisions”

Commenting on a recent investigation of the effect of in-medium corrections to the pion dispersion relation, we point out that the description (hence the conclusions) might be affected if a more refined (and consistent) {Delta}N{sup {minus}1} model was employed, primarily due to the appearance of two pionic modes (rather than only one) whose character ({pi} or {Delta}N{sup {minus}1}) changes with momentum. {copyright} {ital 1997} {ital The American Physical Society}

Dilepton production in ultrarelativistic heavy-ion collisions.

The production of dileptons is studied within a hadronic transport model. We investigate the sensitivity of the dilepton spectra to the initial configuration of the hadronic phase in a ultrarelativistic heavy-ion collision. Possible in-medium corrections due to the modifications of pions and the pion form factor in a hadronic gas are discussed. \textcopyright{} 1996 The American Physical Society.

Semiclassical delta self-energy

We present a semiclassical approach of the Δ self-energy. We show that the in-medium corrections of the Δ width issued from the Pauli blocking and the coupling to the 2N-1h continuum are in good agreement with the previous approaches and particularly with the quantum Δ-h model even for light nuclei. We separate out the different sources of the imaginary part of the self-energy. The predominant corrections come from two antagonistic origins: the Pauli blocking and the contribution to the two-nucleon emission channel, the latter being model dependent. We further show that the non-diagonal spin matrix elements of the self-energy, generated by its tensor component, are mostly due to the Pauli blocking.

Multifragmentation, fragment flow, and the nuclear equation of state.

The quantum molecular dynamic method is used to study multifragmentation and fragment flow and their dependence on in-medium cross sections, momentum dependent interactions, and the nuclear equation of state, for collisions of $^{197}\mathrm{Au}$${+}^{197}$Au and $^{93}\mathrm{Nb}$${+}^{93}$Nb in the bombarding energy regime from 100 to 800A MeV. Time and impact parameter dependence of the fragment formation and their implications for the conjectured liquid-vapor phase transition are investigated. We find that the inclusive fragment mass distribution is independent of the equation of state and exhibits a power-law behavior Y(A)\ensuremath{\sim}${A}^{\mathrm{\ensuremath{-}}\ensuremath{\tau}}$ with an exponent \ensuremath{\tau}\ensuremath{\approxeq}-2.3. True multifragmentation events are found in central collisions for energies ${E}_{\mathrm{lab}\mathrm{\ensuremath{\sim}}30--200}$ MeV/nucleon. The associated light fragment (d,t,\ensuremath{\alpha}) to proton ratios increase with the multiplicity of charged particles and decrease with energy, in agreement with recent experiments. The calculated absolute charged particle multiplicities, the multiplicities of intermediate mass (Ag4) fragments, and their respective rapidity distributions do compare well with recent 4\ensuremath{\pi} data, but are quite insensitive to the equation of state.On the other hand, these quantities depend sensitively on the nucleon-nucleon scattering cross section, and can be used to determine \ensuremath{\sigma} experimentally. The transverse momentum flow of the complex fragments increases with the stiffness of the equation of state. Reduced (in-medium) n-n scattering cross sections reduce the fragment flow. Momentum dependent interactions increase the fragment flow. It is shown that the measured fragment flow at 200A MeV can be reproduced in the model. We find that also the increase of the ${p}_{x}$/A values with the fragment mass is in agreement with experiments. The calculated fragment flow is too small as compared to the plastic ball data, if a soft equation of state with in-medium corrections (momentum dependent interactions plus reduced cross sections) is employed. An alternative, most intriguing resolution of the puzzle about the stiffness of the equation of state could be an increase of the scattering cross sections due to precritical scattering in the vicinity of a phase transition.

Particle clustering and Mott transitions in hot nuclear matter at finite temperature

The properties of hot nuclear matter are calculated by considering the Coulomb interaction in a Debye-Thomas-Fermi approach. It is shown that the inclusion of the Coulomb forces implies a decrease of the cluster bound-state energy and a lowering of the nuclear density at the cluster surface. The Coulomb interaction together with consideration of the in-medium corrections leads to significant modification of the abundances of larger clusters compared with the frequently used law-of-mass-action approach.

Expanding fireballs and the account of the Pauli quenching for the deuteron production

Describing the expanding fireballs in a relativistic gas dynamical approach the formation of deuterons is calculated under consideration of inmedium corrections. The theoretical results are in good agreement with experimental data.

Deuteron production — an entropy puzzle?

We reconsider the possibility of deducing the entropy attained in energetic heavy-ion reactions by means of the measured abundancies of compounds. In-medium corrections for the effective binding forces are seen to sensitivity influence the balance between nucleons and compounds. They reduce the deuteron production to rates close to the observed values with entropy values in line with conventional expectations.